The plots in lexicographical order tell the story of the analysis of determining the functional relationship of the response variable perseat based on the potential explanatory variable(s):
A qqnorm plot of the response variable perseat marginally excluding the presence of potential explantory variable(s). The quantiles certainly do not appear to fit a normal distribution of any mean and variance due to the points forming a roughly exponential shape.
boxcox(perseat ~ 1)
Since the above qqnorm plot certainly indicates a non-normal distribution it is necessary to determine a more appropriate fit. However, what transformation will provide a more reasonable fit? A boxcox transformation will likely be informative of the most appropriate transformation of perseat that will allow a normal distribution to fit the response data.
From the plot above, the logarithmic transformation appears most appropriate for our perseat data appropriately balancing the reasonable confidence interval of optimality from the boxcox plot and simplicity/understanding within the model. None the less, constructing a qqnorm plot of the log base 2 perseat data will aid in confirming this conclusion. A logarithmic tranformation appears appropriate from this plot even with the observation that the tails appear heavy. No model is correct, but a normal model should be effictive at modeling this log transformed data.
qqmath(~log2perseat | area)
Now that the appropriate transformation on the response variable has been determined, it is time to determine how our explanatory variable(s) affect our transformed response variable. The explanatory variable that is perceived to have the greatest impact both individually and interactively is area, ordered by, us the data analysts, by single day price, due to its comprehendable and direct implications on rotational orientation and distance away from the field. However, since area is a categorical variable, the graphing choices are limited and cannot be observed as an xyplot.
xyplot(log2perseat ~ row)
The next explanatory variable to test was row as it also affects distance away from the field, but as a quantitative variable as oppose to the qualitative variable of area. Thus, an xyplot could be observed as opposed to merely a qqnorm plot conditioned on area. Without conditioning on area, there is high variability within each row. None the less, an obvious negative linear trend can still be observed without conditioning on area.
xyplot(log2perseat ~ row | area)
Now, to observe this quantitative response variable against probably our most useful quantiative explanatory variable of row conditioned on probably our most useful explanatory variable of area.
xyplot(log2perseat ~ price)
Each level of single day ticket price takes on 1 or more unique levels of area as now catgegorized by we, the data analysts, to essentially translate area from a categorical variable to a quantitative variable as valued by those that within the Chicago Bears organization that set the single day ticket prices. This now gives us a moderate outlet to observe our quantitative response variable against area as a pseudo quantitative explanatory variable in an xyplot.